Interpolation by Bivariate Quadratic Polynomials and Applications to the Scattered Data Interpolation Problem

Author(s):  
Francesco Dell’Accio ◽  
Filomena Di Tommaso
1999 ◽  
Vol 68 (226) ◽  
pp. 733-748 ◽  
Author(s):  
Kurt Jetter ◽  
Joachim Stöckler ◽  
Joseph D. Ward

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 44239-44262 ◽  
Author(s):  
Nur Nabilah Che Draman ◽  
Samsul Ariffin Abdul Karim ◽  
Ishak Hashim

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 159 ◽  
Author(s):  
Fatin Amani Mohd Ali ◽  
Samsul Ariffin Abdul Karim ◽  
Azizan Saaban ◽  
Mohammad Khatim Hasan ◽  
Abdul Ghaffar ◽  
...  

This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C1 continuity everywhere, we impose a rational corrected scheme that results from convex combination between three local schemes. The final interpolant has the form quintic numerator and quadratic denominator. We test the scheme by considering the established dataset as well as visualizing the rainfall data and digital elevation in Malaysia. We compare the performance between the proposed scheme and some well-known schemes. Numerical and graphical results are presented by using Mathematica and MATLAB. From all numerical results, the proposed scheme is better in terms of smaller root mean square error (RMSE) and higher coefficient of determination (R2). The higher R2 value indicates that the proposed scheme can reconstruct the surface with excellent fit that is in line with the standard set by Renka and Brown’s validation.


Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1101 ◽  
Author(s):  
Qiuyan Xu ◽  
Zhiyong Liu

Surface modeling is closely related to interpolation and approximation by using level set methods, radial basis functions methods, and moving least squares methods. Although radial basis functions with global support have a very good approximation effect, this is often accompanied by an ill-conditioned algebraic system. The exceedingly large condition number of the discrete matrix makes the numerical calculation time consuming. The paper introduces a truncated exponential function, which is radial on arbitrary n-dimensional space R n and has compact support. The truncated exponential radial function is proven strictly positive definite on R n while internal parameter l satisfies l ≥ ⌊ n 2 ⌋ + 1 . The error estimates for scattered data interpolation are obtained via the native space approach. To confirm the efficiency of the truncated exponential radial function approximation, the single level interpolation and multilevel interpolation are used for surface modeling, respectively.


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